Related papers: A Mathematical Framework for Resilience: Dynamics,…

Maintaining stability in feedback systems, from aircraft and autonomous robots to biological and physiological systems, relies on monitoring their behavior and continuously adjusting their inputs. Incremental damage can make such control…

Infrastructure systems play a critical role in providing essential products and services for the functioning of modern society; however, they are vulnerable to disasters and their service disruptions can cause severe societal impacts. To…

Making decisions about the structure of a future military fleet is a challenging task. Several issues need to be considered such as the existence of multiple competing objectives and the complexity of the operating environment. A particular…

Consequences of the basic and most evident consistency requirement-that measured events cannot happen and not happen at the same time-are shortly reviewed. Particular emphasis is given to event forecast and event control. As a consequence,…

Accountability aims to provide explanations for why unwanted situations occurred, thus providing means to assign responsibility and liability. As such, accountability has slightly different meanings across the sciences. In computer science,…

Modeling and analyzing security of networked systems is an important problem in the emerging Science of Security and has been under active investigation. In this paper, we propose a new approach towards tackling the problem. Our approach is…

A dynamical systems approach to turbulence envisions the flow as a trajectory through a high-dimensional state space transiently visiting the neighbourhoods of unstable simple invariant solutions (E. Hopf, Commun. Appl. Maths 1, 303, 1948).…

A common problem in risk analysis is to characterize the overall security of a system of valuable assets (e.g., government buildings or communication hubs), and to suggest measures to mitigate any hazards or security threats. Currently,…

The vast majority of today's critical infrastructure is supported by numerous feedback control loops and an attack on these control loops can have disastrous consequences. This is a major concern since modern control systems are becoming…

Resilience in cyber-physical systems of systems (CPSoS) is often assessed using static indices or point-in-time metrics that do not adequately account for the temporal evolution of risk following a disruption. This paper formalizes…

We present a risk-aware formalism for evaluating system trajectories in the presence of uncertain interactions between the system and its environment. The proposed formalism supports reasoning under uncertainty and systematically handles…

Extreme events, such as rogue waves, earthquakes and stock market crashes, occur spontaneously in many dynamical systems. Because of their usually adverse consequences, quantification, prediction and mitigation of extreme events are highly…

Algorithmic robustness refers to the sustained performance of a computational system in the face of change in the nature of the environment in which that system operates or in the task that the system is meant to perform. Below, we motivate…

Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems like the power grid, social, and neural networks, and they form the…

In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics…

The paper investigates dynamical systems for which the derivative of some positive-definite function along the solutions of this system depends on so-called density function. In turn, such dynamical systems are called density systems. The…

Harmonic theory provides a mathematical framework to describe the structure, behavior, evolution and emergence of harmonic systems. A harmonic system is context aware, contains elements that manifest characteristics either collaboratively…

This paper proposes strategies for designing a system whose computational model is subject to aleatory and epistemic uncertainty. Aleatory variables, which are caused by randomness in physical parameters, are draws from a possibly unknown…

In this paper, we present a unified framework for decision making under uncertainty. Our framework is based on the composite of two risk measures, where the inner risk measure accounts for the risk of decision given the exact distribution…

This work proposes a notion of robust reachability of one set from another set under constant control. This notion is used to construct a control strategy, involving sequential set-to-set reachability, which guarantees robust global…